## 43 Citations

### Pseudodeterminants and perfect square spanning tree counts

- Mathematics
- 2013

The pseudodeterminant pdet(M) of a square matrix is the last nonzero coefficient in its characteristic polynomial; for a nonsingular matrix, this is just the determinant. If ∂ is a symmetric or…

### BARYCENTRIC CHARACTERISTIC NUMBERS

- Mathematics
- 2015

If G is the category of finite simple graphs G = (V,E), the linear space V of valuations on G has a basis given by the f-numbers vk(G) counting complete subgraphs Kk+1 in G. The barycentric…

### Green functions of Energized complexes

- MathematicsArXiv
- 2020

It is proved here that the quadratic energy expression summing over all pairs h(x)^* h(y) of intersecting sets is a signed sum of squares of Green function entries.

### An Elementary Dyadic Riemann Hypothesis

- MathematicsArXiv
- 2018

It is shown that for every one-dimensional simplicial complex G, the functional equation zeta(s)=zeta(-s) holds, where zeta (s) is the Zeta function of the positive definite squared connection operator L^2 of G.

### A combinatorial expression for the group inverse of symmetric M-matrices

- MathematicsSpecial Matrices
- 2021

Abstract By using combinatorial techniques, we obtain an extension of the matrix-tree theorem for general symmetric M-matrices with no restrictions, this means that we do not have to assume the…

### Gauss-Bonnet for multi-linear valuations

- MathematicsArXiv
- 2016

We prove Gauss-Bonnet and Poincare-Hopf formulas for multi-linear valuations on finite simple graphs G=(V,E) and answer affirmatively a conjecture of Gruenbaum from 1970 by constructing higher order…

### The zeta function for circular graphs

- MathematicsArXiv
- 2013

It is proved that the roots of zeta(n,s) converge for n to infinity to the line Re(s)=1/2 in the sense that for every compact subset K in the complement of this line, and large enough n, no root of the zeta function zeta(-s) is in K.

### The Kuenneth formula for graphs

- MathematicsArXiv
- 2015

The Kuenneth identity is proven using Hodge describing the harmonic forms by the product f g of harmonic forms of G and H and uses a discrete de Rham theorem given by a combinatorial chain homotopy between simplicial and de Ram cohomology.

### The Tree-Forest Ratio

- MathematicsArXiv
- 2022

. The number of rooted spanning forests divided by the number of spanning rooted trees in a graph G with Kirchhoﬀ matrix K is the spectral quantity τ ( G ) = det(1 + K ) / det( K ) of G by the matrix…

### A Singular Woodbury and Pseudo-Determinant Matrix Identities and Application to Gaussian Process Regression

- MathematicsArXiv
- 2022

An e-cient algorithm and numerical analysis is provided for the presented determinant identities and their advantages in certain conditions which are applicable to computing log-determinant terms in likelihood functions of Gaussian process regression.

## References

SHOWING 1-10 OF 61 REFERENCES

### On the Coefficients of the Characteristic Polynomial

- Mathematics
- 1998

It is a well-known fact that the first and last non-trivial coefficients of the characteristic polynomial of a linear operator are respectively its trace and its determinant. This work shows how to…

### The McKean-Singer Formula in Graph Theory

- MathematicsArXiv
- 2013

The McKean-Singer formula chi(G) = str(exp(-t L)) which holds for any complex time t, and is proved to allow to find explicit pairs of non-isometric graphs which have isospectral Dirac operators.

### Matrix-Forest Theorems

- MathematicsArXiv
- 2006

A graph-theoretic interpretation is provided for the adjugate to the Laplacian characteristic matrix for weighted multigraphs and the analogous theorems for (multi)digraphs are established.

### The zeta function for circular graphs

- MathematicsArXiv
- 2013

It is proved that the roots of zeta(n,s) converge for n to infinity to the line Re(s)=1/2 in the sense that for every compact subset K in the complement of this line, and large enough n, no root of the zeta function zeta(-s) is in K.

### Selfsimilarity in the Birkhoff sum of the cotangent function

- Mathematics
- 2012

We prove that the Birkhoff sum S(n)/n = (1/n) sum_(k=1)^(n-1) g(k A) with g(x) = cot(Pi x) and golden ratio A converges in the sense that the sequence of functions s(x) = S([ x q(2n)])/q(2n) with…

### On the Dimension and Euler characteristic of random graphs

- MathematicsArXiv
- 2011

It is shown here that the average dimension E[dim] is a computable polynomial of degree n(n-1)/2 in p and the explicit formulas for the signature polynomials f and g allow experimentally to explore limiting laws for the dimension of large graphs.

### The Theory of Matrices

- Mathematics
- 1984

Volume 2: XI. Complex symmetric, skew-symmetric, and orthogonal matrices: 1. Some formulas for complex orthogonal and unitary matrices 2. Polar decomposition of a complex matrix 3. The normal form of…

### Self-similarity and growth in Birkhoff sums for the golden rotation

- Mathematics
- 2011

We study Birkhoff sums with at the golden mean rotation number with continued fraction pn/qn. The summation of such quantities with logarithmic singularity is motivated by critical KAM phenomena…

### An Introduction to Linear Algebra

- Mathematics
- 2006

Class notes on vectors, linear combination, basis, span. 1 Vectors Vectors on the plane are ordered pairs of real numbers (a, b) such as (0, 1), (1, 0), (1, 2), (−1, 1). The plane is denoted by R,…